James Branch Cabell (1879-1958)
Something About Eve: A Comedy of Fig-Leaves (1927)

A southern gentleman exchanges bodies with a deity.

An extract:
“Therefore, I repeat, I will take over your natural body, just as that first Glaum once took over my body; and I will take over all your body’s imbroglios, even with your mistress,—who can hardly be more tasking to get along with than are the seven official wives and the three hundred and fifty-odd concubines I am getting rid of.”
“You,” Gerald said, morosely, “do not know Evelyn Townsend.”
“I trust,” the Sylan stated, more gallantly, “to have that privilege to-morrow.”
It was in this way the bargain was struck.

Thanks are due to Ralph Sir Edward who found the text and did a lot of proof-reading.